QuestionIn 2002, the median home price was \$ 184,200. Which standard deviation is most plausible: \$ 2000, \$ 60,000, or \$ 1,000,000? Why?
Studdy Solution
STEP 1
Assumptions1. The median selling price of new homes in a state in200 was $184,200.
. We are trying to find the most plausible value for the standard deviation.
3. The standard deviation is a measure of the amount of variation or dispersion of a set of values.
4. A negative standard deviation is not possible because it's a square root of the variance, and the square root of a negative number is not a real number.
5. The standard deviation cannot be larger than the range of the data, which is the difference between the largest and smallest values.
STEP 2
Let's analyze each optionA. 60,000 and 1,000,000 is the most plausible value, because all the other values are too small for house prices, which have a large spread. C. 2,000 is too small, and 11,000 is the most plausible, because half the houses are less than the median value and the values of 1,000,000 are both implausibly large.
STEP 3
First, we can rule out option D because the standard deviation cannot be negative.
STEP 4
Next, we can rule out option B because a standard deviation of 184,200. The standard deviation cannot be larger than the range of the data, and it's unlikely that the range of home prices is over $1,000,000.
STEP 5
Between options A and C, we need to consider what the standard deviation represents. It's a measure of the spread of the data. A standard deviation of 2,000 of the median, which seems too small for home prices.
STEP 6
On the other hand, a standard deviation of 60,000 of the median. This seems more plausible given the variability in home prices.
STEP 7
Therefore, the most plausible value for the standard deviation is $60,000, which is option C.
The correct answer is C. 2,000 is too small, and $1,000,000 is implausibly large.
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